报告人：郑佳悦，博士，华南农业大学

腾讯会议：614-318-236

报告时间：2025年6月27日14:00-15:00

报告摘要：

We study a free boundary problem modeling the growth of nonnecrotic

tumors with angiogenesis, where the model has a nonlinear boundary value condition for the nutrient concentration. We first study spherically symmetric version of this model. We prove that there exists a unique spherically symmetric stationary solution which is asymptotically stable under spherically symmetric perturbation. Next we make rigorous analysis to the spherically asymmetric version of this model. By using some abstract theory of parabolic differential equations in Banach manifold, we prove that this free boundary problem is locally well-posed in little Hölder spaces and the radial stationary solution is asymptotically stable in case the surface tension coefficient γ is larger than a threshold value, whereas unstable in case γ is less than this threshold value. Finally, by using the bifurcation method, we show that nonradial stationary solutions do exist when the surface tension coefficient γ takes values in small neighborhoods of certain eigenvalues of the linearized problem at the radial stationary solution.

邀请人：吴俊德